Integrand size = 21, antiderivative size = 13 \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=\frac {15}{62 \left (-\frac {5}{e}+x\right )} \]
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Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 27, 32} \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=-\frac {15 e}{62 (5-e x)} \]
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Rule 12
Rule 27
Rule 32
Rubi steps \begin{align*} \text {integral}& = -\left (\left (15 e^2\right ) \int \frac {1}{1550-620 e x+62 e^2 x^2} \, dx\right ) \\ & = -\left (\left (15 e^2\right ) \int \frac {1}{62 (-5+e x)^2} \, dx\right ) \\ & = -\left (\frac {1}{62} \left (15 e^2\right ) \int \frac {1}{(-5+e x)^2} \, dx\right ) \\ & = -\frac {15 e}{62 (5-e x)} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=\frac {15 e}{62 (-5+e x)} \]
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Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00
method | result | size |
gosper | \(\frac {15 \,{\mathrm e}}{62 \left (x \,{\mathrm e}-5\right )}\) | \(13\) |
risch | \(\frac {15 \,{\mathrm e}}{62 \left (x \,{\mathrm e}-5\right )}\) | \(13\) |
meijerg | \(-\frac {3 \,{\mathrm e}^{2} x}{310 \left (1-\frac {x \,{\mathrm e}}{5}\right )}\) | \(15\) |
norman | \(\frac {3 \,{\mathrm e}^{2} x}{62 \left (x \,{\mathrm e}-5\right )}\) | \(16\) |
parallelrisch | \(\frac {3 \,{\mathrm e}^{2} x}{62 \left (x \,{\mathrm e}-5\right )}\) | \(16\) |
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Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=\frac {15 \, e}{62 \, {\left (x e - 5\right )}} \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.15 \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=\frac {15 e^{2}}{62 x e^{2} - 310 e} \]
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Time = 0.18 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.15 \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=\frac {15 \, e^{2}}{62 \, {\left (x e^{2} - 5 \, e\right )}} \]
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Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=\frac {15 \, e}{62 \, {\left (x e - 5\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int -\frac {15 e^2}{1550-620 e x+62 e^2 x^2} \, dx=\frac {15\,\mathrm {e}}{62\,\left (x\,\mathrm {e}-5\right )} \]
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